Universally catenarian domains of D+M type, II
Let T be a domain of the form K+M, where K is a field and M is a maximal ideal of T. Let D be a subring of K such that R=D+M is universally catenarian. Then D is universally catenarian and K is algebraic over k, the quotient field of D. If [K:k]<∞, then T is universally catenarian. Consequently,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000212 |
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| Summary: | Let T be a domain of the form K+M, where K is a field and M is a maximal ideal
of T. Let D be a subring of K such that R=D+M is universally catenarian. Then D is
universally catenarian and K is algebraic over k, the quotient field of D. If [K:k]<∞, then T is
universally catenarian. Consequently, T is universally catenarian if R is either Noetherian or a
going-down domain. A key tool establishes that universally going-between holds for any domain
which is module-finite over a universally catenarian domain. |
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| ISSN: | 0161-1712 1687-0425 |